EDIT: On Saturday 9/6 another prime was found. They're also keeping mum about what this one is. But I know this one too...

EDIT2: Every new Mersenne prime also means a new perfect number is discovered; counting these two new Mersenne primes, there are now 46 known perfect numbers, all of them even. (It is conjectured, but not proven, that all perfect numbers are even.) To go from a Mersenne prime (which is of the form 0b111...11, where there are a prime number of 1's) to its corresponding perfect number, tack on one fewer number of 0's onto the end of the number: e.g., 0b11 (3, the first Mersenne prime) becomes 0b110 (6, the first perfect number;) 0b111 (7, the second Mersenne prime) becomes 0b11100 (28, the second perfect number) etc. (The proof that such numbers are perfect is simple; there is a more complicated proof that all even perfect numbers are of this form.)

Q53: Say you have three integers between 0 - 9. You have the equation: A! + B! +
C! = ABC (where ABS is a three digit numbers, not A * B * C). Find A, B, and C
that satisfies this equation.

Interesting. But I'd like to modify the question a little.

Q53': Say you have three integers between 0 - 9. You have the equation: A! + B! +
C! = A * B * C.Find A, B, and C
that satisfies this equation.

Astute readers will notice that A, B, and C are interchangeable. Nonetheless there is a unique solution (modulo swapping A, B, and C.)

I'm much less interested in the answer to this question (I know the answer) than I am in the quality of the program used to find the answer. (I tried finding the answer by hunt-and-peck, then gave up and wrote a program - I find the program to be more interesting than the answer.) Try to find the solution as efficiently as possible (without cheating.)

I suspect that the following even more general problem has the same unique solution, which would be very interesting indeed. This is the kind of thing where programs fail, and the mathematical mind becomes necessary again:

Q53'': Say you have three integers that are >= 0. You have the equation: A! + B! +
C! = A * B * C.
Find A, B, and C
that satisfies this equation.